Idea Transcript
Hazen-Williams Formula In the absence of solid scientific data, engineers in the past have experimented with and used empirical equations for determination of friction losses in pipe flow. Many of these equations were developed over the early years but most have fallen into disuse. Due to the difficulty in using the D’Arcy-Weisback equation for pipe flow one singular example still endures, which is the Hazen-Williams formula. Hazen-Williams is simpler to use than D’Arcy-Weisbach where you are solving for flowrate, pressure drop or velocity dependent on the flow. The D’Arcy-Weisbach formula is generally considered more accurate and is valid for any liquid or gas. The Hazen-Williams method is very popular, especially among civil engineers, because of its ease of use and its friction coefficient “C” is not a function of velocity or pipe diameter. Its validity depends on the successful selection of the constant friction loss coefficient “C”, which is a function of pipe material, pipe linings and pipe age to indicate the roughness of a pipe interior. The higher the C factor, the smoother the pipe. Typical values of the roughness coefficient “C” is given in the table following this definition. The Hazen-Williams equation has narrow applicable ranges for Reynolds numbers and pipe sizes. The equation is generally valid for pipe sizes 3 in. (75 mm) and larger, for water flowing at temperatures of between 40° to 75ºF (21° to 24°C) and pressures up to 175 psi (1.2 MPa). The level of error when the Hazen-Williams equation is used outside its data ranges is significant. In this case, the D’Arcy-Weisbach formula must be used. The Hazen-Williams equation is commonly used for pressure drop calculations in American fire sprinkler systems, water distribution systems, and irrigation systems where conditions are mostly constant.
Hazen-Williams Formula Solving for psi pressure drop per 100 feet of pipe × Q1.85 Pd = 4.52 C1.85 × d4.87 Solving for total psi pressure drop in system 1.85 1.85 × Q1.8655 Td = 0.002082 L 100 C d Solving for velocity V = 1.318 × C × R0.63 × S0.54 Solving for flow rate Q = 0.849 × C × A × R0.63 × S0.54 Solving for friction head loss per 100 feet of type, SI units. 6.05 × Q1.85 f= C1.85 × d 4.87
where Q = quantity rate of flow, gpm (Lpm) C = roughness coefficient, dimensionless d = inside pipe diameter, in. (mm) f = friction head loss in ft. hd./100 ft. of pipe (m per 100m) Pd = pressure drop, psi/100 feet of pipe R = hydraulic radius, feet (m) V = Velocity, feet per second A = cross section area, in (mm) Td = Total drop in system, psi L = Total length of pipe run, ft.
Plumbing Engineering and Design Handbook of Tables
73
2
Sizing and Capacity (Natural Gas) Gas): U.S./English
Maximum Capacity in Cubic Feet of Gas Per Hour (Natural Gas) Material: Steel, ASTM A53 – Schedule 40
Nominal Actual OD WT Actual ID Feet
1 0
10 20 30 40 50 60 70 80 90 100 125 150 175 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1,000 1,100 1,200 1,300 1,400 1,500 1,600 1,700 1,800 1,900 2,000
1032
Inlet Pressure = 5.0 psi Pressure Drop = 3.5 psi • Specific Gravity 0.60 • Temperature 70°F Pipe Size (inch) ½ ¾ 1 1¼ 1½ 2 0.840 1.050 1.315 1.660 1.900 2.375 0.109 0.113 0.133 0.140 0.145 0.154 0.622 0.824 1.049 1.380 1.610 2.067 Cubic Feet of Gas per Hour 3276 2251 1808 1547 1371 1243 1143 1064 998 943 835 757 696 648 574 520 479 445 418 395 375 358 342 329 317 306 296 287 279 271 258 246 235 226 218 210 204 197 192 186
6850 4708 3781 3236 2868 2598 2390 2224 2087 1971 1747 1583 1456 1355 1201 1088 1001 931 874 825 784 748 716 688 663 640 619 600 583 567 539 514 492 473 455 440 426 413 401 390
12903 8868 7121 6095 5402 4895 4503 4189 3930 3713 3291 2981 2743 2552 2262 2049 1885 1754 1646 1554 1476 1408 1349 1296 1248 1205 1166 1131 1098 1068 1015 968 927 891 858 828 802 777 755 734
26491 18207 14621 12514 11091 10049 9245 8601 8070 7623 6756 6121 5631 5239 4643 4207 3870 3601 3378 3191 3031 2891 2769 2660 2563 2475 2395 2322 2255 2193 2083 1987 1903 1828 1761 1701 1646 1596 1550 1507
39692 27280 21907 18749 16617 15056 13852 12886 12091 11421 10122 9171 8438 7850 6957 6303 5799 5395 5062 4781 4541 4332 4149 3986 3840 3708 3588 3479 3379 3286 3121 2978 2851 2739 2639 2548 2466 2391 2322 2259
76443 52539 42190 36110 32003 28997 26677 24818 23286 21996 19494 17663 16250 15117 13398 12140 11169 10390 9749 9209 8746 8344 7990 7676 7395 7141 6911 6700 6507 6329 6011 5735 5492 5276 5082 4908 4750 4605 4472 4350
2½ 2.875 0.203 2.469 121838 83738 67245 57553 51008 46217 42519 39556 37114 35058 31071 28152 25900 24095 21355 19349 17801 16560 15538 14677 13939 13298 12735 12234 11786 11382 11015 10679 10371 10087 9580 9140 8753 8409 8101 7823 7570 7340 7128 6933
American Society of Plumbing Engineers
Steel. ASTM A53 — Schedule 40
Maximum Capacity in Cubic Feet of Gas Per Hour (Natural Gas) Material: Steel, ASTM A53 – Schedule 40 (Continued)
Nominal Actual OD WT Actual ID Feet
10 20 30 40 50 60 70 80 90 100 125 150 175 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1,000 1,100 1,200 1,300 1,400 1,500 1,600 1,700 1,800 1,900 2,000
Inlet Pressure = 5.0 psi Pressure Drop = 3.5 psi • Specific Gravity 0.60 • Temperature 70°F Pipe Size (inch) 3 4 5 6 8 10 3.500 4.500 5.563 6.625 8.625 10.750 0.216 0.237 0.258 0.280 0.322 0.365 3.068 4.026 5.047 6.065 7.981 10.020 Cubic Feet of Gas per Hour 215387 148035 118877 101743 90173 81703 75166 69928 65611 61976 54928 49769 45786 42595 37752 34206 31469 29276 27468 25946 24642 23509 22513 21628 20836 20121 19472 18879 18335 17833 16937 16158 15473 14865 14320 13829 13383 12975 12601 12256
439322 301943 242471 207524 183925 166649 153315 142630 133825 126410 112035 101512 93390 86881 77001 69769 64186 59713 56027 52922 50263 47952 45919 44115 42499 41040 39716 38507 37397 36373 34545 32957 31560 30320 29209 28207 27297 26466 25703 24999
794795 546258 438665 375440 332746 301492 277368 258038 242108 228694 202687 183649 168955 157180 139306 126221 116122 108029 101360 95744 90932 86751 83075 79810 76886 74248 71852 69664 67656 65804 62497 59624 57097 54853 52843 51030 49384 47880 46500 45227
1286957 884518 710299 607924 538792 488185 449124 417823 392030 370309 328198 297371 273577 254511 225568 204381 188028 174924 164125 155032 147241 140470 134517 129231 124496 120224 116345 112803 109551 106553 101198 96544 92453 88820 85565 82629 79963 77529 75294 73233
Plumbing Engineering and Design Handbook of Tables
2644205 1817347 1459394 1249052 1107012 1003033 922778 858467 805471 760843 674321 610984 562097 522923 463457 419926 386326 359402 337215 318531 302523 288613 276381 265520 255792 247015 239045 231766 225085 218925 207923 198362 189955 182490 175804 169772 164294 159292 154700 150466
4802582 3300787 2650649 2268613 2010629 1821776 1676011 1559205 1462950 1381894 1224747 1109710 1020919 949768 841762 762697 701672 652770 612473 578538 549463 524198 501983 482255 464587 448645 434169 420949 408815 397626 377643 360278 345010 331451 319308 308351 298402 289316 280976 273286
12 12.750 0.375 12.000 7707103 5297048 4253717 3640631 3226624 2923555 2689634 2502185 2347718 2217641 1965454 1780844 1638353 1524172 1350845 1223964 1126031 1047555 982886 928428 881769 841223 805573 773915 745561 719978 696748 675532 656059 638104 606035 578168 553666 531907 512420 494837 478871 464289 450905 438565
1033
1 0
Hazen-Williams Equation: PEX Tubing, ASTM F877
Flow Rate, Velocity, and Friction Loss (Water) Material: PEX Tubing, ASTM F877
Coefficient of Friction, C = 150
2
OD = Outside Diameter (in.) • ID = Inside Diameter (in.) • WT = Wall Thickness (in.)
½" PEX
OD = 0.625 • ID = 0.485 • WT = 0.070 Flow Rate (gpm)
Velocity (ft/sec)
Pressure Loss (psi/100')
1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 15.00 16.00
1.74 3.47 5.21 6.95 8.68 10.42 12.16 13.89 15.63 17.37 19.10 20.84 22.58 24.31 26.05 27.79
1.4448 5.2085 11.0276 18.7767 28.3728 39.7546 52.8736 67.6899 84.1697 102.2839 122.0067 143.3153 166.1891 190.6094 216.5590 244.0222
Plumbing Engineering and Design Handbook of Tables
¾" PEX
OD = 0.875 • ID = 0.681 • WT = 0.097 Flow Rate (gpm)
1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00 18.00 19.00 20.00 21.00 22.00 23.00 24.00 25.00 26.00 27.00 28.00 29.00 30.00 31.00 32.00 33.00
Velocity (ft/sec)
Pressure Loss (psi/100')
0.88 1.76 2.64 3.52 4.40 5.29 6.17 7.05 7.93 8.81 9.69 10.57 11.45 12.33 13.21 14.09 14.97 15.86 16.74 17.62 18.50 19.38 20.26 21.14 22.02 22.90 23.78 24.66 25.54 26.43 27.31 28.19 29.07
0.2767 0.9974 2.1116 3.5955 5.4330 7.6124 10.1245 12.9616 16.1173 19.5859 23.3625 27.4428 31.8228 36.4989 41.4679 46.7267 52.2725 58.1028 64.2151 70.6071 77.2768 84.2219 91.4407 98.9314 106.6921 114.7212 123.0173 131.5787 140.4040 149.4918 158.8409 168.4499 178.3175
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